The LCM of two numbers is 14 times their . . .

Question : The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then the other number will be

a) 70

b) 75

c) 78

d) 80

Doubt by Yathartha

Solution :

LCM = 14HCF — (1)

LCM + HCF = 600 — (2)

a = 280
b = ?
14HCF + HCF = 600 [Using (1)]

15 HCF = 600
HCF = 600/15
HCF = 40

LCM+40 = 600
LCM = 600-40
LCM = 560

We know,
a×b = LCM×HCF
280×b = 560×40
b = (560×40)/280
b = 560/7
b = 80

Hence, d) would be the correct option.

Class 10